The Republican mayor turned Donald Trump advisor credited himself for lowering taxes, getting 600,000 people off welfare and straightening out a "good deal" of the education system in NY. This was in response to Tapper pressing Giuliani on Trump apologizing for his support of the idea in past years, citing the concerns of many black voters and Trump's recent appeals.

In a pretty startling pivot from last week, Donald Trump surrogates Rudy Giuliani told CNN's Jake Tapper that Trump is backing off from his stance supporting mass deportations and thinks that families with some legal citizen children should be allowed to stay.

"Having been the mayor of a city that was rotting when I took it over - on the front cover of Time magazine [in 1990 was] "The rotting of the Big Apple" - because of years of liberal-Democratic policies, NY could be Detroit if I hadn't turned it around", Giuliani told CNN's "State of the Union" Sunday. The former mayor of New York City said that such a scenario does not represent the "kind of America (Trump) wants".

Giuliani acknowledged confusion in the wake of Trump's aggressive and emotional immigration speech last week in Phoenix, an event that included appearances by parents whose children have been killed by migrants in the country illegally.

Former Mayor Rudy Giuliani said the Big Apple would be rotten if he hadn't been elected mayor. We don't know who will be left.

"If you read that speech carefully, that speech is consistent with what he has said in the past, and it leaves a very big opening for what will happen with the people that remain here in the United States after the criminals are removed and after the border is secure", Giuliani said.

Trump's critics say it's a charade to suggest there is any softening in Trump's immigration policies. "That's the whole point here, that we've actually never tried this", Conway said.

Trump's vice presidential pick, Gov. Pence, on Sunday, deflected questions about the fate of those undocumented immigrants who haven't committed additional crimes in the United States, on NBC's "Meet the Press". "And so at least he's trying to solve a problem".

The comments by Conway and Pence brought criticism from the Clinton campaign.

"Donald Trump has stated very clearly throughout his campaign that he will deport everyone who is undocumented, something that was reinforced in his speech in Arizona last Wednesday", Clinton campaign manager Robby Mook said in a statement Sunday afternoon. "Immigrant families know the meanings of "humane" and "fair" and can see straight through their cynical ploys". Yet, by definition, unauthorised entry into the country criminalises immigrants according to hardliners like Mr. Trump.